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Syllabus: Op-amp Circuits: Amplifiers, summers, differentiators, integrators, active filters, Schmitt triggers and oscillators.
15 hand-picked visual resources on this topic, 1 of them little-known gems — under each card, look for See it. Every link is checked against the live site before it ships.
The two golden rules
With negative feedback present, no current enters the inputs and the two input terminals sit at the same voltage. Almost every linear op-amp question falls out of these two facts plus KCL at the inverting node.
only when negative feedback is present
Where marks are lost
With positive feedback — a Schmitt trigger — the virtual short does not hold; the output is at a rail.
See it
Integrators and differentiators
Where the capacitor sits decides which one it is: in the feedback path it integrates, in the input path it differentiates.
Schmitt trigger
Positive feedback gives two switching thresholds, and the gap between them is the hysteresis that rejects noise.
Oscillators
Sustained oscillation needs a loop gain of exactly one with zero net phase shift. The two standard RC oscillators each have a fixed gain condition worth remembering.
Barkhausen criterion
Summers, difference and instrumentation amplifiers
All of these follow from the virtual short and no input current. A summing amplifier is just several inputs meeting at the virtual ground, so each contributes independently of the others — which is what makes weighted-resistor DACs work.
Active filters
An op-amp lets an network be cascaded without loading the previous stage, so the order adds up cleanly. Recognise the topology first: feedback through a capacitor is a low pass (an integrator), a capacitor in the input path is a high pass.
The non-ideal op-amp
The golden rules assume infinite gain and infinite bandwidth. Real limits show up as three separate effects, and a question usually isolates one: finite gain-bandwidth caps the closed-loop bandwidth, slew rate caps the output rate, and offsets shift DC.
Comparators and precision circuits
An op-amp without feedback is a comparator: the output slams to a rail. Putting a diode inside the feedback loop divides its drop by the open-loop gain, which is how millivolt-level signals get rectified at all.
C in feedback
C at the input
See it
See it
See it
inverting summer; inputs do not interact
non-inverting summer — the inputs do load each other
difference amplifier; mismatch is what limits CMRR
three-op-amp instrumentation amplifier: one resistor sets the gain
See it
first order, dB/dec beyond it
And dB at if the stages are identical.
Sallen–Key second order
peaks; is critically damped
which is why a bare differentiator amplifies noise
Where marks are lost
An ideal integrator has infinite DC gain and saturates on any input offset. The practical one puts a large resistor across the feedback capacitor — and that resistor is why it stops integrating below .
See it
constant — ten times the gain, a tenth of the bandwidth
full-power bandwidth; beyond it the sine turns into a triangle
gain error from finite open-loop gain
why a balancing resistor is put in the non-inverting leg
Where marks are lost
Slew rate and bandwidth are different limits. A small signal can be faster than the bandwidth allows and never hit the slew limit; a large one hits the slew limit well inside the bandwidth.
See it
open loop; no virtual short applies
the diode drop divided by the open-loop gain
the one test that tells a comparator from an amplifier